Computational approaches to modeling dynamos in galaxies.

Galaxies are observed to host magnetic fields with a typical total strength of around 15  $\mu$ G. A coherent large-scale field constitutes up to a few microgauss of the total, while the rest is built from strong magnetic fluctuations over a wide range of spatial scales. This represents sufficient magnetic energy for it to be dynamically significant. Several questions immediately arise: What is the physical mechanism that gives rise to such magnetic fields? How do these magnetic fields affect the formation and evolution of galaxies? In which physical processes do magnetic fields play a role, and how can that role be characterized? Numerical modelling of magnetized flows in galaxies is playing an ever-increasing role in finding those answers. We review major techniques used for these models. Current results strongly support the conclusion that field growth occurs during the formation of the first galaxies on timescales shorter than their accretion timescales due to small-scale turbulent dynamos. The saturated small-scale dynamo maintains field strengths at only a few percent of equipartition with turbulence. This is in contradiction with the observed magnitude of turbulent fields, but may be reconciled by the further contribution to the turbulent field of the large-scale dynamo. The subsequent action of large-scale dynamos in differentially rotating discs produces field strengths observed in low redshift galaxies, where it reaches equipartition with the turbulence and has substantial power at large scales. The field structure resulting appears consistent with observations including Faraday rotation and polarisation from synchrotron and dust thermal emission. Major remaining challenges include scaling numerical models toward realistic scale separations and Prandtl and Reynolds numbers.